Scattering in three-dimensional fuzzy space

We develop scattering theory in a non-commutative space defined by a $su(2)$ coordinate algebra. By introducing a positive operator valued measure as a replacement for strong position measurements, we are able to derive explicit expressions for the probability current, differential and total cross-sections. We show that at low incident energies the kinematics of these expressions is identical to that of commutative scattering theory. The consequences of spacial non-commutativity are found to be more pronounced at the dynamical level where, even at low incident energies, the phase shifts of the partial waves can deviate strongly from commutative results. This is demonstrated for scattering from a spherical well. The impact of non-commutativity on the well's spectrum and on the properties of its bound and scattering states are considered in detail. It is found that for sufficiently large well-depths the potential effectively becomes repulsive and that the cross-section tends towards that of hard sphere scattering. This can occur even at low incident energies when the particle's wave-length inside the well becomes comparable to the non-commutative length-scale.Comment: 12 pages, 6 figure

Eigenvalue distributions from a star product approach

We use the well-known isomorphism between operator algebras and function spaces equipped with a star product to study the asymptotic properties of certain matrix sequences in which the matrix dimension $D$ tends to infinity. Our approach is based on the $su(2)$ coherent states which allow for a systematic 1/D expansion of the star product. This produces a trace formula for functions of the matrix sequence elements in the large-$D$ limit which includes higher order (finite-$D$) corrections. From this a variety of analytic results pertaining to the asymptotic properties of the density of states, eigenstates and expectation values associated with the matrix sequence follows. It is shown how new and existing results in the settings of collective spin systems and orthogonal polynomial sequences can be readily obtained as special cases. In particular, this approach allows for the calculation of higher order corrections to the zero distributions of a large class of orthogonal polynomials.Comment: 25 pages, 8 figure

Duality constructions from quantum state manifolds

The formalism of quantum state space geometry on manifolds of generalised coherent states is proposed as a natural setting for the construction of geometric dual descriptions of non-relativistic quantum systems. These state manifolds are equipped with natural Riemannian and symplectic structures derived from the Hilbert space inner product. This approach allows for the systematic construction of geometries which reflect the dynamical symmetries of the quantum system under consideration. We analyse here in detail the two dimensional case and demonstrate how existing results in the AdS_2/CFT_1 context can be understood within this framework. We show how the radial/bulk coordinate emerges as an energy scale associated with a regularisation procedure and find that, under quite general conditions, these state manifolds are asymptotically anti-de Sitter solutions of a class of classical dilaton gravity models. For the model of conformal quantum mechanics proposed by de Alfaro et. al. the corresponding state manifold is seen to be exactly AdS_2 with a scalar curvature determined by the representation of the symmetry algebra. It is also shown that the dilaton field itself is given by the quantum mechanical expectation values of the dynamical symmetry generators and as a result exhibits dynamics equivalent to that of a conformal mechanical system.Comment: 25 Pages, References Adde

Spectrum of the three dimensional fuzzy well

We develop the formalism of quantum mechanics on three dimensional fuzzy space and solve the Schr\"odinger equation for a free particle, finite and infinite fuzzy wells. We show that all results reduce to the appropriate commutative limits. A high energy cut-off is found for the free particle spectrum, which also results in the modification of the high energy dispersion relation. An ultra-violet/infra-red duality is manifest in the free particle spectrum. The finite well also has an upper bound on the possible energy eigenvalues. The phase shifts due to scattering around the finite fuzzy potential well have been calculated

Determining the elements of the operations management transformation model for the monitoring and breaching of the Great Brak River Mouth system

The prime challenge to those responsible for the management of South Africa’s estuaries is to maintain their viability in the face of ever increasing pressures. It is important that we learn to appreciate the value of estuaries and that we act wisely to manage them for sustainable use. Any operation must have the adequate resources to perform the duties and the correct processes must be followed. The purpose of this research is to determine whether the current inputs and processes needed for the monitoring and breaching of the Great Brak River Mouth system are sufficient to adhere to the output objectives of a healthy estuary together with safeguarding of properties. The research methodology for this study comprised the following steps: Firstly, a literature study was performed to identify the key elements of the operation management transformation model. Operations management deals with the output of any business, in other words the conversion of inputs to create certain outputs and they do this by a process of transformation. Secondly, extensive literature study was performed in order to access material regarding effective estuary and river mouth management. Thirdly, the current situation at Great Brak was assessed to determine whether the current inputs and processes are in place and if additional or altered inputs and processes are needed

Symptomatology and Anatomy of Stemgrooving (Legno Riccio) 1n the Grape Vine

External and anatomical differences between organs affected and unaffected by stemgrooving were studied on the wine grape cultivar Chenin blanc and the table grape cultivars Barlinka and Almeria. Cultivar susceptibility, graft transmissibility as well as the effect of the disease on the percentage of take and growth in: the nursery were studied. The probability of an association with other virus diseases was considered. Abnormal behaviour of the vascular cambium of infected vines gave rise to hypertrophy, hyperplasia, hypoplasia and parenchymatoses in the secondary xylem and phloem. In diseased tissues dift'erentiation of pbeDogen proceeded abnormally deep into the phloem rays. Graft transmission was detected anatomically within six months. The disease was found in all the vine growing districts of the Western Cape. Anatomical.studies showed that the disease had been present for many years. A negative effect on the percentage of t:'tKe and growth in the nursery was, recorded. A probable-relationship with corky bark was indicated anatomically and by indexing with LN33

Non-perturbative flow equations from continuous unitary transformations

We use a novel parameterization of the flowing Hamiltonian to show that the flow equations based on continuous unitary transformations, as proposed by Wegner, can be implemented through a nonlinear partial differential equation involving one flow parameter and two system specific auxiliary variables. The implementation is non-perturbative as the partial differential equation involves a systematic expansion in fluctuations, controlled by the size of the system, rather than the coupling constant. The method is applied to the Lipkin model to construct a mapping which maps the non-interacting spectrum onto the interacting spectrum to a very high accuracy. This function is universal in the sense that the full spectrum for any (large) number of particles can be obtained from it. In a similar way expectation values for a large class of operators can be obtained, which also makes it possible to probe the stucture of the eigenstates.Comment: 24 pages, 13 figure

Availability of infective larvae of parasitic nematodes of sheep grazing on Kikuyu (Pennisetum clandestinum) pastures in the winter rainfall area

Thirteen groups of 4 South African mutton Merinos grazed for 4 weeks with the flock on Kikuyu pastures and were slaughtered for total and differential worm counts at necropsy. Subsequently 12 groups of 8 week tracers grazed on the pastures and were killed for worm counts post mortem. The following were present in most sheep: Teladorsagia (syn. Ostertagia) circumcincta, Trichostrongylus axei, Trichostrongylus colubriformis, Dictyocaulus filaria and Oesophagostomum venulosum. Haemonchus contortus, Nematodirus spathiger and Trichuris skrjabini were less frequently recovered. Optimal conditions for infestation of grazing sheep occurred from June (late autumn)-October (spring) when mean temperatures in any 4 week period were 40 mm of rain fell on 8 or more separate days. When the mean temperatures exceeded 20 °C pastures were safe, sheep acquiring< 1 000 worms in 4 weeks.The articles have been scanned in colour with a HP Scanjet 5590; 600dpi. Adobe Acrobat XI Pro was used to OCR the text and also for the merging and conversion to the final presentation PDF-format.lmchunu2014mn201